摘要
We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in L p α ,where L p α is the weighted Banach space of complex continuous functions f defined on the real axis R satisfying ＋∞ ∞ ｜f（t）｜ p e -α（t） dt） 1/p ,1 p ∞,and α（t） is a nonnegative continuous function defined on the real axis R.In this paper,the upper density of the sequence which forms the exponential polynomials is not required to be finite.In the study of weighted polynomial approximation,consideration of the case is new.
We take a new approach to obtaining necessary and sufficient conditions for the incompleteness of exponential polynomials in L p α ,where L p α is the weighted Banach space of complex continuous functions f defined on the real axis R satisfying ＋∞ ∞ ｜f（t）｜ p e -α（t） dt） 1/p ,1 p ∞,and α（t） is a nonnegative continuous function defined on the real axis R.In this paper,the upper density of the sequence which forms the exponential polynomials is not required to be finite.In the study of weighted polynomial approximation,consideration of the case is new.
基金
Supported by the Basic Research Foundation of Yunnan Province (Grant No. 2009ZC013X)
the Basic Research Foundation of Education Bureau of Yunnan Province (Grant No. 09Y0079)
